Operads, configuration spaces and quantization
2011 (English)In: Bulletin of the Brazilian Mathematical Society, ISSN 1678-7544, E-ISSN 1678-7714, Vol. 42, no 4, 683-781 p.Article in journal (Refereed) Published
We review several well-known operads of compactified configuration spaces and construct several new such operads, (C) over bar, in the category of smooth manifolds with corners whose complexes of fundamental chains give us (i) the 2-coloured operad of A(infinity)-algebras and their homotopy morphisms, (ii) the 2-coloured operad of L(infinity)-algebras and their homotopy morphisms, and (iii) the 4-coloured operad of open-closed homotopy algebras and their homotopy morphisms. Two gadgets - a (coloured) operad of Feynman graphs and a de Rham field theory on (C) over bar - are introduced and used to construct quantized representations of the (fundamental) chain operad of (C) over bar which are given by Feynman type sums over graphs and depend on choices of propagators.
Place, publisher, year, edition, pages
2011. Vol. 42, no 4, 683-781 p.
Poisson geometry, homotopy Lie algebras, configuration spaces
IdentifiersURN: urn:nbn:se:su:diva-70636DOI: 10.1007/s00574-011-0034-3ISI: 000297742900009OAI: oai:DiVA.org:su-70636DiVA: diva2:483006
authorCount :12012-01-242012-01-232012-01-24Bibliographically approved